Mann-Whitney U Test Calculator

The Mann-Whitney U Test (also called the Wilcoxon rank-sum test) is a non-parametric statistical test used to compare two independent groups. It tests whether one group tends to have higher values than the other, without assuming the data follows a normal distribution. It works by ranking all observations together and comparing the rank sums between groups.

Use the Mann-Whitney U Test when your data does not meet the normality assumption required by the independent samples t-test. It is also preferred when your sample sizes are small, when data is ordinal rather than continuous, or when significant outliers are present that would distort parametric results.

The null hypothesis (H₀) states that the distributions of both groups are equal — equivalently, the probability that a randomly selected value from Group 1 exceeds a randomly selected value from Group 2 equals 0.5. The alternative hypothesis states that the groups differ (or that one group tends to be higher than the other for one-sided tests).

The U statistic counts the number of times a value from Group 1 exceeds a value from Group 2 across all possible pairings. Two U values (U1 and U2) are calculated, and the smaller one is typically reported. A very small or very large U relative to the maximum possible value indicates a significant difference between groups.

For larger samples (n > 20 for either group), this calculator uses a normal approximation with continuity correction to convert the U statistic into a Z score, then derives the p-value from the standard normal distribution. For small samples, the test uses exact methods based on the rank distribution.

The most common significance level is 0.05, meaning you accept a 5% probability of incorrectly rejecting the null hypothesis. Use α = 0.01 or 0.001 for more conservative tests when false positives are costly, such as in medical or clinical research. Use α = 0.10 for exploratory analyses where you want to flag potential effects.

A two-sided test checks whether the two groups differ in either direction (Group 1 could be higher or lower than Group 2). A one-sided test checks a specific direction — either Group 1 > Group 2 or Group 1 < Group 2. Choose a one-sided test only if you have a strong prior reason to expect the direction of the difference.

Yes. When ties exist in the data, average ranks are assigned to the tied values. This calculator applies the standard tie-correction to the variance formula used in the Z-score approximation, ensuring the p-value remains accurate even when ties are present in your dataset.